What must be the potential difference across the plates of the capacitor filled with a dielectric so that it stores the same amount of electrical energy as the empty capacitor?

Explanation:

The electrical energy stored in the empty capacitor is defined as:

Where is the potential difference across the plates of the capacitor and is its capacitance.

The capacitance of the capacitor with a dielectric is given by:

The electrical energy stored in the capacitor filled with a dielectric is:

We have . Thus:

Replacing (1) and solving for :

freezing

deposition

condensation

explanation;

melting also called fusion is the process where solid becomes liquid, sublimation is the process where solid becomes gaseous without first changing to liquid, deposition involves change from gaseous to solid state, freezing involves change from liquid to solid, boiling or evaporation involves change of liquid to gaseous state, while condensation is the change from gaseous state to liquid state.

endothermic reactions involves absorption of heat from the surroundings or the environment while exothermic reactions involves loss of heat energy to the surroundings.

in this case, sublimation, evaporation and melting are endothermic reactions (gain energy from the environment) while, freezing, deposition and condensation are exothermic (loss of energy to the surroundings) reactions.

your answer is, orbit around the nucleus